Function problem

For discussing Olympiad Level Algebra (and Inequality) problems
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Gautampl
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Function problem

Unread post by Gautampl » Thu Apr 10, 2014 8:57 am

$f(x)=\sqrt{x^2+1}$

$f(g(x))=3|x|$

Then $g(x)=?$
:?:

Nirjhor
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Re: Function problem

Unread post by Nirjhor » Fri Apr 25, 2014 3:35 pm

Let $f^{-1}(x)=y$, then $f(f^{-1}(x))=f(y)=\sqrt{y^2+1}=x$ which implies $y=\pm \sqrt{x^2-1}$. So $g(x)=f^{-1}(3|x|)=\pm\sqrt{9x^2-1}$.
- What is the value of the contour integral around Western Europe?

- Zero.

- Why?

- Because all the poles are in Eastern Europe.


Revive the IMO marathon.

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